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On the matrix (I + X) -1 <= I

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Author Info
Engwerda, Jacob (Tilburg University, Center for Economic Research)

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Abstract

In this note we consider the question under which conditions all entries of the matrix I-(I+X)-1 are nonnegative in case matrix X is a real positive definite matrix. Sufficient conditions are presented as well as some necessary conditions. One sufficient condition is that matrix X-1 is an inverse M-matrix. A class of matrices for which the inequality holds is presented.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 120.

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Date of creation: 2005
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Handle: RePEc:dgr:kubcen:2005120

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C00 - Mathematical and Quantitative Methods - - General - - - General

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  1. Engwerda, Jacob & Douven, Rudy C., 2005. "On the sensitivity matrix of the Nash bargaining solution," Discussion Paper 35, Tilburg University, Center for Economic Research. [Downloadable!]
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